We construct four new exact level (size) alpha tests for testing the equality
of k distributions, which can be conveniently used in high dimensional low sample
size setup based on clustering. These tests are easy to implement and distribution-free.
Under mild conditions, we have proved the consistency of these tests as the dimension
d of each observation grows to infinity, whereas the sample size remains fixed.
We also apply step-down-procedure (1979) for multiple testing. Details are in
Biplab Paul, Shyamal K De and Anil K Ghosh (2020); Soham Sarkar and Anil K Ghosh (2019)